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arXiv:2005.14500

Topological second-order spin-3/2 liquids with hinge Fermi arcs

Y. X. Zhao, Yen-Wen Lu, Shengyuan A. Yang

Published May 29, 2020• 3 citations
arXivHTMLPDF

Abstract

We present an exactly solvable spin-3/2 model defined on a pentacoordinated three-dimensional graphite lattice, which realizes a novel quantum spin liquid with second-order topology. The exact solutions are described by Majorana fermions coupled to a background $\mathbb{Z}_2$ gauge field, whose ground-state flux configuration gives rise to an emergent off-centered spacetime inversion symmetry. The symmetry protects topologically nontrivial band structures for the Majorana fermions, particularly including nodal-line semimetal phases with twofold topological charges: the second Stiefel-Whitney number and the quantized Berry phase. The former leads to rich topological phenomena on the system boundaries. There are two nodal-line semimetal phases hosting hinge Fermi arcs located on different hinges, and they are separated by a critical Dirac semimetal state with surface helical Fermi arcs. In addition, we show that rich symmetry/topology can be explored in our model by simply varying the lattice or interaction arrangement. As an example, we discuss how to achieve a topological gapped phase with surface Dirac points.

DOI
10.48550/arxiv.2005.14500

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We present an exactly solvable spin-3/2 model defined on a pentacoordinated three-dimensional graphite lattice, which realizes a novel quantum spin liquid with second-order topology. The exact solutions are described by Majorana fermions coupled to a background Z2\mathbb{Z}_2Z2​ gauge field, whose ground-state flux configuration gives rise to an emergent off-centered spacetime inversion symmetry. The symmetry protects topologically nontrivial band structures for the Majorana fermions, particularly including nodal-line semimetal phases with twofold topological charges: the second Stiefel-Whitney number and the quantized Berry phase. The former leads to rich topological phenomena on the system boundaries. There are two nodal-line semimetal phases hosting hinge Fermi arcs located on different hinges, and they are separated by a critical Dirac semimetal state with surface helical Fermi arcs. In addition, we show that rich symmetry/topology can be explored in our model by simply varying the lattice or interaction arrangement. As an example, we discuss how to achieve a topological gapped phase with surface Dirac points.
Recently, there has been much effort in understanding topological phases of matter with gapless bulk excitations, which are characterized by topological invariants and protected intrinsic boundary states. Here we show that topological semimetals of Majorana fermions arise in exactly solvable Kitaev spin models on a series of three-dimensional lattices. The ground states of these models are quantum spin liquids with gapless nodal spectra of bulk Majorana fermion excitations. It is shown that these phases are topologically stable as long as certain discrete symmetries are protected. The corresponding topological indices and the gapless boundary states are explicitly computed to support these results. In contrast to previous studies of noninteracting systems, the phases discussed in this work are novel examples of gapless topological phases in interacting spin systems.
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The formation of quantum spin liquids in frustrated magnets represents an exciting possibility due to the rather exotic features they harbor, including fractionalized excitations and emergent gauge fields. \nUnfortunately, they are notoriously difficult to study as there are often no good analytical methods available and quantum Monte Carlo simulations are hindered by the negative sign problem. \nThe Kitaev honeycomb model is a notable exception of a frustrated quantum model which is exactly solvable and which hosts a number of distinct quantum spin liquid ground states. \nAs such, it allows for a rare opportunity to study the physics of spin liquids with full analytical control. \n \nIn this thesis, we study the fractionalization of spin-1/2 moments into Majorana fermions and an emergent Z2 gauge field in a generalization of the Kitaev honeycomb model to a number of three-dimensional lattices. \nWhile the excitations of the gauge field are always gapped, the fermionic quasiparticles may exhibit a gapless dispersion, forming fully two-dimensional Fermi surfaces, symmetry protected nodal lines, or topological Weyl nodes. \nWe show that one can deduce rather general constraints on the possible gapless excitations by making use of an object called the projective symmetry group. \nIn doing so we provide a scheme for classifying the various gapless Kitaev spin liquids. \nA thorough analysis is carried out for a number of these spin liquids, primarily investigating the stability of the gapless modes and the novel features resulting from their sometimes non-trivial topology, as well as their effects on certain equal-time correlation functions.
Dirac semimetals, with their protected Dirac points, present an ideal platform for realizing intrinsic topological superconductivity. In this work, we investigate superconductivity in a two-dimensional, square-lattice nonsymmorphic Dirac semimetal. In the normal state near half-filling, the Fermi surface consists of two distinct pockets, each enclosing a Dirac point at a time-reversal invariant momentum (X=(π,0)\textbf{X}=(π,0)X=(π,0) and Y=(0,π)\textbf{Y}=(0,π)Y=(0,π)). Considering an on-site repulsive and nearest-neighbor attractive interaction, we use self-consistent mean-field theory to determine the ground-state pairing symmetry. We find that an even-parity, spin-singlet dx2−y2d_{x^{2}-y^{2}}dx2−y2​-wave pairing is favored as it gives rise to a fully gapped superconducting state. Since the pairing amplitude has opposite signs on the two Dirac Fermi pockets, the superconducting state is identified as a second-order topological superconductor. The hallmark of this topological phase is the emergence of Majorana zero modes at the system's boundaries. Notably, the positions of these Majorana modes are highly controllable and can be manipulated simply by tailoring the boundary sublattice terminations. Our results highlight the promise of nonsymmorphic Dirac semimetals for realizing and manipulating Majorana modes.
Three-dimensional Kitaev models -- generalizations of the well known exactly solvable Kitaev honeycomb model -- exhibit a rich variety of quantum spin liquid phases. Their fractionalized excitations are Majorana fermions that may form topological band structures. These can be enriched by lattice symmetries, as shown in the present work. In particular, the authors propose two new instances of Kitaev spin liquids that exhibit nodal chains and 3D Dirac nodes in the bulk. Such crystalline Kitaev spin liquids are direct generalizations of crystalline topological insulators, albeit in an interacting spin system. A potential material realization in metal-organic frameworks is also discussed.